Because Americans copied the practices and traditions of Mexican cowhands, thus becoming the all-too-famous American cowboys. From Wikipedia:
The historic American cowboy of the late 19th century arose from the vaquero traditions of northern Mexico and became a figure of special significance and legend.
It wasn't really the "Mexicans" who influenced the "Americans" but the Spanish who brought the cowboy to the American continents The American cowboys borrowed language, clothing and food, that the Mexican vaqueros used, and one of the things that they did not borrow was their politics.
Vaquero (literal translation for cowboy)
Northern Mexico, including the territories acquired from Mexico during the Texas Revolution and Mexican-American War.
Vaqueros
They were called Vaqueros.
Everything. The cowboy culture is actually of Mexican origin.
mexican vaqueros
The Battle of Chapultepec.
vaquero is spanish for "cowboy". Example One out of every three cowboys in the late 1800s was the Mexican vaquero.
The most important would be the cowboy culture, which was copied from the Mexican 'vaqueros' (literally, cowboys in Spanish) who developed several haciendas in northern Mexico, (nowadays the US Southwest). From there, you have several other traits, such as the rodeo and the Tex-Mex cuisine, based on the traditions from these cowhands.
Vaqueros moved cattle around and aranged many fiesta's
Mexican-American War formally ends in 1848.